Orbital Analysis for matched events on 20210813_212448.559_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 66.14° Bg 38.22° Vg 54.76km/s
mass 0.01031g, abs. mag 0.3
Path Details
------------
start -0.29° 51.80° 109.07km
end   -0.43° 51.63° 97.22km

Orbit Details
-------------
Semimajor axis 2.62A.U., eccentricity 0.66, inclination 109.70°, Period 4.25Y, LA Sun 141.05°, last Perihelion 2021-07-13

Full details below
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Input measurement type: Azimuth +east of due north for meas1, Elevation angle above the horizon for meas2

Uncertainties type:
 Purely geometric uncertainties

Reference JD: 2459440.392228702083
Time: 2021-08-13 21:24:48.559860 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK0001 and UK002W
 Convergence angle = 10.59720 deg
 R.A. =  52.52385  Dec = +58.93624 deg

Best intersection: Stations UK0001 and UK002W with Qconv = 10.60 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =    934732.85 +/- 1443.47 m
 Y =  -3910046.79 +/- 552.14 m
 Z =   5074450.94 +/- 2169.50 m
 Vx =    17541.38 +/- 4273.45 m/s
 Vy =    22561.30 +/- 4347.05 m/s
 Vz =    48007.61 +/- 6258.94 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+4.929779e+05, +1.810398e+05, +7.454985e+05, +1.244581e+06, +2.886188e+05, +1.634960e+06
+1.810398e+05, +7.210304e+04, +2.789811e+05, +4.755586e+05, +1.151861e+05, +6.226296e+05
+7.454985e+05, +2.789811e+05, +1.142444e+06, +1.874223e+06, +4.335462e+05, +2.481623e+06
+1.244581e+06, +4.755586e+05, +1.874223e+06, +4.182125e+06, +9.614097e+05, +5.329729e+06
+2.886188e+05, +1.151861e+05, +4.335462e+05, +9.614097e+05, +2.559702e+05, +1.247798e+06
+1.634960e+06, +6.226296e+05, +2.481623e+06, +5.329729e+06, +1.247798e+06, +6.889954e+06

Timing offsets (from input data):
    UK0001: 0.000000 s
    UK002W: -0.014234 s

Reference point on the trajectory:
  Time: 2021-08-13 21:24:48.559860 UTC
  Lon     = +-0.287046 +/- 0.0218 deg
  Lat     = +51.796081 +/- 0.0132 deg
  Lat geo = +51.612051 +/- 0.0133 deg
  Ht      =  108946.51 +/- 1583.14 m

  JD dynamic   = 2459440.393029442988 
  LST apparent = 283.4447569934 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  52.13497 +/- 4.9592 deg
  Dec       = +59.23532 +/- 0.1974 deg
  Azimuth   =  27.02627 +/- 2.5123 deg
  Elevation = +28.52074 +/- 1.3259 deg
  Vavg      =  55.42314 +/- 5.3873 km/s
  Vinit     =  55.86987 +/- 7.1686 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  51.77049 +/- 4.9592 deg
  Dec       = +59.03360 +/- 0.1974 deg
  Azimuth   =  27.33024 +/- 2.5123 deg
  Elevation = +28.45531 +/- 1.3259 deg
  Vavg      =  55.54083 +/- 5.3873 km/s
  Vinit     =  55.98756 +/- 7.1686 km/s
Radiant (geocentric, J2000):
  R.A.   =  52.42958 +/- 5.0652 deg
  Dec    = +58.58610 +/- 0.1674 deg
  Vg     =  54.75680 +/- 7.2943 km/s
  Vinf   =  55.86987 +/- 7.1686 km/s
  Zc     =  61.64323 +/- 1.3296 deg
  Zg     =  62.33112 +/- 1.4951 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  66.13893 +/- 3.1947 deg
  Bg     = +38.22071 +/- 0.8634 deg
  Vh     =  37.59487 +/- 6.3936 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  92.94125 +/- 13.2845 deg
  Bh     = +64.30711 +/- 1.4017 deg
  Vh_x   =   0.83634 +/- 4.4665 km/s
  Vh_y   = -16.27768 +/- 3.6671 km/s
  Vh_z   = -33.87790 +/- 5.1938 km/s
Orbit:
  La Sun = 141.045308 +/- nan deg
  a      =   2.624648 +/- 11.5699 AU
  e      =   0.655145 +/- 0.5601
  i      = 109.703103 +/- 4.8086 deg
  peri   = 136.950590 +/- 24.1856 deg
  node   = 141.043701 +/- 0.0004 deg
  Pi     = 277.994290 +/- 24.1853 deg
  q      =   0.905123 +/- 0.0916 AU
  f      =  43.045361 +/- 24.1858 deg
  M      =   7.319225 +/- nan deg
  Q      =   4.344173 +/- 23.1637 AU
  n      =   0.231792 +/- 0.4104 deg/day
  T      =   4.252137 +/- 485215420.2727 years
  Last perihelion JD = 2459408.816269 (2021-07-13 07:35:25.600889) +/- 12.7661 days
  Tj     =   1.621067 +/- 3.3769
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +2.525975e-02, +9.330705e-03, +1.681793e+00, -5.128362e-07, +4.274078e-02, +6.900663e-03
q   , +9.330705e-03, +4.513701e-03, +7.345923e-01, -2.276327e-07, +1.977179e-02, +3.089634e-03
Tp  , +1.681793e+00, +7.345923e-01, +1.244829e+02, -3.818659e-05, +3.274322e+00, +5.166081e-01
node, -5.128362e-07, -2.276327e-07, -3.818659e-05, +1.191152e-11, -1.010341e-06, -1.612188e-07
peri, +4.274078e-02, +1.977179e-02, +3.274322e+00, -1.010341e-06, +8.725835e-02, +1.369395e-02
i   , +6.900663e-03, +3.089634e-03, +5.166081e-01, -1.612188e-07, +1.369395e-02, +2.182674e-03

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 22.360680
 a2 = 0.000000

Mean time residuals from time vs. length:
  Station with reference time: UK0001
  Avg. res. = 3.936e-05 s
  Stddev    = 6.27e-03 s

Begin point on the trajectory:
  Lon =    -0.285617 +/- 0.0220 deg
  Lat =    51.797818 +/- 0.0133 deg
  Ht  = 109066.45 +/- 1593.89 m
End point on the trajectory:
  Lon =    -0.428829 +/- 0.0107 deg
  Lat =    51.625251 +/- 0.0056 deg
  Ht  = 97215.71 +/- 729.40 m

Stations
--------
        ID, Ignored, Lon +E (deg), Lat +N (deg),  Ht (m), Jacchia a1, Jacchia a2,  Beg Ht (m),  End Ht (m), +/- Obs ang (deg), +/- V (m), +/- H (m), Persp. angle (deg), Weight, FOV Beg, FOV End, Comment
    UK0001,   False,    -1.778230,    50.857470,   24.00,  17.447564,   0.000000,   109066.45,    97215.71,          0.020559,     62.68,      8.43,              17.98, 1.0000,    True,    True, {"ff_name": "FF_UK0001_20210813_212447_944_0115712.fits"}
    UK002W,   False,    -2.374601,    51.371449,   48.00,  37.792824,   0.000000,   106206.46,    97917.25,          0.024809,     77.39,      3.12,              39.28, 1.0000,    True,    True, {"ff_name": "FF_UK002W_20210813_212446_858_0109056.fits"}

Points
------
 No, Station ID,  Ignore,  Time (s),                   JD,     meas1,     meas2, Azim +E of due N (deg), Alt (deg), Azim line (deg), Alt line (deg), RA obs (deg), Dec obs (deg), RA line (deg), Dec line (deg),       X (m),       Y (m),       Z (m), Latitude (deg), Longitude (deg), Height (m),  Range (m), Length (m), State vect dist (m),  Lag (m), Vel (m/s), Vel prev avg (m/s), H res (m), V res (m), Ang res (asec), AppMag, AbsMag
  0,     UK0001,       0,  0.000000, 2459440.392228702083,  20.46423,  54.93697,               44.27910,  35.53206,        44.25879,       35.57094,     20.46423,     +54.93697,      20.43071,      +54.97459,   934811.72, -3909945.35,  5074666.78,      51.797818,       -0.285617,  109066.45,  184468.25,       0.00,              251.19,   213.93,      0.00,           54661.86,     17.95,   -134.85,         152.12,  +2.82,  +1.49
  1,     UK0001,       0,  0.039984, 2459440.392229164951,  20.04924,  54.88117,               44.51966,  35.67962,        44.52657,       35.66643,     20.04924,     +54.88117,      20.06081,      +54.86842,   934019.72, -3910964.00,  5072499.23,      51.780368,       -0.300135,  107862.29,  182058.08,    2522.53,             2271.35,     0.20,  63088.60,           54661.86,     -6.16,     45.14,          51.61,  +2.11,  +0.81
  2,     UK0001,       0,  0.080040, 2459440.392229628284,  19.80281,  54.76595,               44.74046,  35.71535,        44.72842,       35.73858,     19.80281,     +54.76595,      19.78294,      +54.78828,   933435.07, -3911715.97,  5070899.14,      51.767481,       -0.310893,  106973.86,  180279.18,    4384.67,             4133.48,  -375.59,  46488.28,           54661.86,     10.56,    -78.57,          90.70,  +1.12,  -0.16
  3,     UK0001,       0,  0.120056, 2459440.392230091617,  19.44082,  54.67960,               44.98659,  35.82156,        44.98310,       35.82831,     19.44082,     +54.67960,      19.43542,      +54.68607,   932717.00, -3912639.53,  5068933.91,      51.751647,       -0.324063,  105883.23,  178098.31,    6671.75,             6420.57,  -324.20,  57154.21,           54661.86,      3.05,    -22.53,          26.34,  +1.10,  -0.15
  4,     UK0001,       0,  0.160092, 2459440.392230554949,  19.04627,  54.55707,               45.28239,  35.92031,        45.27709,       35.93063,     19.04627,     +54.55707,      19.03785,      +54.56693,   931912.38, -3913674.40,  5066731.83,      51.733897,       -0.338795,  104661.89,  175658.77,    9234.47,             8983.28,     1.71,  64010.33,           56508.87,      4.60,    -33.97,          40.25,  +0.94,  -0.28
  5,     UK0001,       0,  0.200132, 2459440.392231018282,  18.73137,  54.44198,               45.53545,  35.98901,        45.52191,       36.01563,     18.73137,     +54.44198,      18.70864,      +54.46730,   931258.84, -3914514.98,  5064943.19,      51.719473,       -0.350787,  103670.40,  173678.68,   11316.04,            11064.85,  -153.75,  51987.19,           56390.27,     11.65,    -86.47,         103.63,  +1.02,  -0.18
  6,     UK0001,       0,  0.240132, 2459440.392231481615,  18.30101,  54.35837,               45.81125,  36.13059,        45.81813,       36.11706,     18.30101,     +54.35837,      18.31403,      +54.34553,   930490.78, -3915502.83,  5062841.16,      51.702515,       -0.364847,  102505.86,  171356.07,   13762.32,            13511.13,    57.73,  61156.97,           56858.26,     -5.94,     43.33,          52.64,  +0.77,  -0.40
  7,     UK0001,       0,  0.280160, 2459440.392231944483,  17.94812,  54.24759,               46.07837,  36.22101,        46.08498,       36.20794,     17.94812,     +54.24759,      17.96097,      +54.23523,   929816.87, -3916369.60,  5060996.79,      51.687628,       -0.377199,  101484.63,  169320.28,   15908.74,            15657.56,   -32.20,  53623.15,           56783.69,     -5.68,     41.34,          50.83,  +0.71,  -0.43
  8,     UK0001,       0,  0.320212, 2459440.392232408281,  17.59218,  54.10582,               46.37736,  36.29433,        46.37216,       36.30472,     17.59218,     +54.10582,      17.58418,      +54.11559,   929111.29, -3917277.11,  5059065.73,      51.672036,       -0.390120,  100415.98,  167192.21,   18156.05,            17904.86,   -22.59,  56109.78,           56703.93,      4.41,    -32.37,          40.31,  +0.65,  -0.47
  9,     UK0001,       0,  0.360240, 2459440.392232871614,  17.15363,  53.97379,               46.70525,  36.41270,        46.70408,       36.41506,     17.15363,     +53.97379,      17.15301,      +53.97599,   928320.59, -3918294.08,  5056901.75,      51.654555,       -0.404574,   99219.14,  164812.20,   20674.44,            20423.25,   259.44,  62915.66,           57002.17,      0.99,     -7.22,           9.11,  +0.60,  -0.48
 10,     UK0001,       0,  0.400272, 2459440.392233334947,  16.78019,  53.85092,               46.99521,  36.50808,        46.99386,       36.51083,     16.78019,     +53.85092,      16.77937,      +53.85348,   927649.03, -3919157.82,  5055063.81,      51.639702,       -0.416870,   98203.19,  162793.10,   22813.38,            22562.19,   161.79,  53430.73,           57002.47,      1.14,     -8.32,          10.63,  +0.74,  -0.32
 11,     UK0001,       0,  0.440324, 2459440.392233798280,  16.43269,  53.70462,               47.29675,  36.57792,        47.28324,       36.60563,     16.43269,     +53.70462,      16.40921,      +53.73033,   926995.96, -3919997.79,  5053276.46,      51.625251,       -0.428829,   97215.71,  160832.47,   24893.45,            24642.26,     4.16,  51934.20,           56807.59,     11.22,    -82.77,         107.12,  +2.03,  +1.00
  0,     UK002W,       0,  0.094791, 2459440.392229243647, 359.79754,  36.74584,               72.46572,  34.58377,        72.46795,       34.61758,    359.79754,     +36.74584,     359.76486,      +36.76710,   932929.84, -3912365.77,  5069516.44,      51.756342,       -0.319903,  106206.46,  183762.98,       0.00,             5742.63,   409.43,      0.00,           54569.80,     -4.53,   -108.48,         121.87,  +5.50,  +4.18
  1,     UK002W,       0,  0.134799, 2459440.392229706515, 359.53183,  36.57994,               72.78883,  34.63099,        72.78706,       34.60510,    359.53183,     +36.57994,     359.55735,      +36.56367,   932519.63, -3912893.38,  5068393.74,      51.747294,       -0.327497,  105583.56,  182756.87,    1306.56,             7049.20,  -519.25,  32657.56,           54569.80,      3.31,     82.65,          93.36,  +4.31,  +3.00
  2,     UK002W,       0,  0.214991, 2459440.392230635043, 358.81948,  35.88631,               73.88217,  34.59156,        73.87907,       34.55333,    358.81948,     +35.88631,     358.85721,      +35.86249,   931149.94, -3914655.04,  5064645.15,      51.717069,       -0.352619,  103505.23,  179438.33,    5669.07,            11411.70,  -637.06,  54400.73,           54569.80,      4.76,    119.90,         137.93,  +3.40,  +2.13
  3,     UK002W,       0,  0.255167, 2459440.392231099773, 358.35563,  35.34529,               74.67606,  34.50591,        74.67630,       34.50848,    358.35563,     +35.34529,     358.35401,      +35.34688,   930180.25, -3915902.23,  5061991.30,      51.695656,       -0.370324,  102035.24,  177120.45,    8757.54,            14500.17,   206.78,  76873.53,           54569.80,     -0.32,     -7.95,           9.27,  +3.59,  +2.35
  4,     UK002W,       0,  0.295239, 2459440.392231563572, 357.99293,  35.01496,               75.21462,  34.50150,        75.21215,       34.47611,    357.99293,     +35.01496,     358.01848,      +34.99930,   929541.36, -3916723.96,  5060242.77,      51.681541,       -0.382042,  101067.28,  175603.14,   10792.44,            16535.07,     2.86,  50781.09,           55594.00,      3.12,     78.00,          91.70,  +1.84,  +0.62
  5,     UK002W,       0,  0.335359, 2459440.392232027836, 357.61984,  34.60873,               75.82889,  34.45209,        75.82718,       34.43577,    357.61984,     +34.60873,     357.63678,      +34.59871,   928820.91, -3917650.58,  5058271.02,      51.665617,       -0.395230,   99976.36,  173906.13,   13087.09,            18829.73,    56.02,  57194.80,           56123.56,      1.99,     49.67,          58.96,  +1.53,  +0.33
  6,     UK002W,       0,  0.375495, 2459440.392232492566, 357.22484,  34.15859,               76.49785,  34.38604,        76.49807,       34.38806,    357.22484,     +34.15859,     357.22426,      +34.15982,   928049.93, -3918642.19,  5056161.00,      51.648570,       -0.409326,   98809.62,  172106.24,   15542.68,            21285.31,   269.21,  61181.69,           56768.71,     -0.25,     -6.08,           7.29,  +1.80,  +0.62
  7,     UK002W,       0,  0.415563, 2459440.392232956365, 356.87840,  33.83345,               77.02335,  34.37538,        77.02020,       34.34886,    356.87840,     +33.83345,     356.90544,      +33.81730,   927459.97, -3919400.99,  5054546.37,      51.635519,       -0.420148,   97917.25,  170737.84,   17421.74,            23164.37,   -90.33,  46896.66,           56407.29,      3.16,     79.34,          95.92,  +3.86,  +2.70

Notes
-----
- Points that have not been taken into consideration when computing the trajectory have '1' in the 'Ignore' column.
- The time already has time offsets applied to it.
- 'meas1' and 'meas2' are given input points.
- X, Y, Z are ECI (Earth-Centered Inertial) positions of projected lines of sight on the radiant line.
- Zc is the observed zenith distance of the entry angle, while the Zg is the entry zenith distance corrected for Earth's gravity.
- Latitude (deg) and Longitude (deg) are in WGS84 coordinates, while Height (m) is in the EGM96 datum. There values are coordinates of each point on the radiant line.
- Jacchia (1955) deceleration equation fit was done on the lag.
- Right ascension and declination in the table are given in the epoch of date for the corresponding JD, per every point.
- 'RA and Dec obs' are the right ascension and declination calculated from the observed values, while the 'RA and Dec line' are coordinates of the lines of sight projected on the fitted radiant line. The coordinates are in the epoch of date, and NOT J2000!. 'Azim and alt line' are thus corresponding azimuthal coordinates.
- 'Vel prev avg' is the average velocity including all previous points up to the given point. For the first 4 points this velocity is computed as the average velocity of those 4 points.